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A064771 Let S(n) = set of divisors of n, excluding n; sequence gives n such that there is a unique subset of S(n) that sums to n. 8
6, 20, 28, 78, 88, 102, 104, 114, 138, 174, 186, 222, 246, 258, 272, 282, 304, 318, 354, 366, 368, 402, 426, 438, 464, 474, 490, 496, 498, 534, 572, 582, 606, 618, 642, 650, 654, 678, 748, 762, 786, 822, 834, 860, 894, 906, 940, 942, 978, 1002, 1014, 1038 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Perfect numbers (A000396) are a proper subset of this sequence. Weird numbers (A006037) are numbers whose proper divisors sum to more than the number, but no subset sums to the number.

Odd elements are rare: the first few are 8925, 32445, 351351, 442365; there are no more below 100 million. See A065235 for more details.

A065205(a(n)) = 1. - Reinhard Zumkeller, Jan 21 2013

LINKS

T. D. Noe, Table of n, a(n) for n=1..200

EXAMPLE

Proper divisors of 20 are 1, 2, 4, 5 and 10. {1,4,5,10} is the only subset that sums to 20, so 20 is in the sequence.

MATHEMATICA

okQ[n_]:= Module[{d=Most[Divisors[n]]}, SeriesCoefficient[Series[ Product[ 1+x^i, {i, d}], {x, 0, n}], n] == 1]; Select[ Range[ 1100], okQ] (* Harvey P. Dale, Dec 13 2010 *)

PROG

(Haskell)

a064771 n = a064771_list !! (n-1)

a064771_list = map (+ 1) $ elemIndices 1 a065205_list

-- Reinhard Zumkeller, Jan 21 2013

CROSSREFS

A005835 gives n such that some subset of S(n) sums to n. Cf. A065205.

Cf. A000396, A006037, A065205, A065235.

Cf. A027751.

Sequence in context: A119425 A006039 A180332 * A006036 A242341 A140738

Adjacent sequences:  A064768 A064769 A064770 * A064772 A064773 A064774

KEYWORD

nonn,easy,nice,changed

AUTHOR

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 19 2001

EXTENSIONS

More terms from Don Reble, Jud McCranie and Naohiro Nomoto, Oct 22 2001

STATUS

approved

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Last modified November 18 12:21 EST 2017. Contains 294891 sequences.